John Pazmino
 2007 April 15
    Each year in March, the American museum of Natural History 
convenes the Isaac Asimov memorial debate. This is a panel discussion 
of a specified topic in astronomy among several experts in the 
profession. On 2007 March 26, the topic for the debate was the 
'Pioneer anomaly'. Because this subject involves both astronomy and 
space travel, the audience had a dozen or so delegates from NYSkies 
and National Space Society. 
    Neil Tyson, Hayden Planetarium director, was the panel moderator. 
Panelists for this debate were: 
        John Anderson, JPL
        Edward Belbruno, Princeton U 
        Gary Kinsella, JPL 
        Irwin Shapiro, H-S CfA 
        Slava Turyshev, JPL 
    Anderson is generally credited with first recognizing and 
announcing the anomaly. He and Turyshev are still actively 
investigating it. Belbruno is an astrodynamicist specializing in 
interplanetary trajectories. Kinsella is an aerospace engineer working 
with spacecraft systems. Shapiro is an astrophysicist and a skeptic of 
alternative solutions beyond current physics.
    The audience, packed into the the Museum's LeFrak Theater and 
overflowing into its Kaufmann Theater, numbered about a full one 
thousand! This is a stunning testament to the vivid science culture 
prevailing in New York City. 
    Due to a generally low-level description and commentary about the 
Pioneer anomaly, there grew up around it a body of pseudoscience and 
faux-fact that at times inhibited a mature investigation of it. The 
public may hear of the Pioneer anomaly wrapped in dialog about 
abnormal science or even nonscience. 
The Pioneer missions
    Pioneer-10 and Pioneer-11 were the first two spacecraft to leave 
the solar system, following their exploration of Jupiter and Saturn. 
Pioneer-10 launched on 1972 March 2; Pioneer-11, 1973 April 5. Altho 
their missions were long ago done, the craft continued to collect 
space environment data and were tracked routinely thru NASA's Deep 
Space Network as probes in the far outer realm of the solar system. 
    Pioneer-11 signals broke off in October 1990. Pioneer-10 may still 
be transmitting but by March 2006 its signal grew too weak to discern 
against the general background radio noise. 
    Following the planet swingbys both craft entered a hyperbolic 
trajectory that carries them almost linearly away from the Sun while 
staying close to the ecliptic plane. By chance, due to their separate 
mission profiles, Pioneer-10 is heading toward western Taurus; 
Pioneer-11, central Scutum. By 2007 Pioneer-10 is about 92AU from the 
Sun; Pioneer-11, 73AU. 
    Both craft were simple, compared to today's payloads, and had only 
a few instruments onboard. They were powered by radioisotope 
generators because at the distance of Jupiter and beyond solar panels 
would collect too little energy. Radioactive power sources were used 
in future deep space missions, like Galileo, Cassini, New Horizons. 
The anomaly
    As the two Pioneers receded from the Sun, their trajectories were 
affected by fewer and fewer natural forces. Notable was the ebbing of 
solar radiation pressure that imparts a slight outward force.  By 
1980m when the ships were well away from other planets or substantial 
mass, their paths were governed essentially only by the gravity field 
of the Sun. As other influences waned, there appeared in the tracking 
data a small acceleration toward the Sun. This is found in the Doppler 
shift of received frequency of the Pioneer rad io transmissions. 
    Only a radial component was ever monitored in the outer solar 
system after the main part of the probe's mission was complete. There 
is substantially no transverse, or proper, motion on the celestial 
sphere because the spaceships are travelling pretty much straight away 
from Sun and Earth. 
    This excess acceleration IS tiny, about 8.7e-10 m/s2. Or 8.7 
ANGSTROMS per square-second!! If this were imparted to a cart at rest, 
how long would it take for the cart to get up to a brisk walking pace 
of 4m/s? About 158-1/2 years! The ability to even detect such a 
minuscule acceleration comes from the extreme maturity of processing 
radio and electronic data. In fact, the excess frequency shift 
associated with this acceleration is only 6e-9Hz/s in the S-band. 
    The effect, now popularly called the 'Pioneer anomaly', was first 
recognized by 1980 but first formally investigated in 1998. Accounts 
about the anomaly can be confusing. The effect is ekked out of data 
from about 1980. It was examined on and off since then thru the 1990s. 
It was first specificly noticed to the world in 1998. Thus, there 
arose a 'coverup' mentality among some space fans. NASA knew about the 
discordant motion and held it secret for over 15 years?! 
    One of the major peculiarities of the Pioneer effect is that 
soonest the craft entered the exit path out of the solar system, the 
magnitude stayed constant over both distance and duration thereafter. 
Other missions 
    We now have four probes in the far edge of the solar system. The 
two Pioneers, Voyager-1, and Voyager-2. The Pioneer effect is not well 
observed in the Voyager probes because they routinely alter their 
speed and orientation by firing jets. The two Pioneers are spin-
stabilized so their radio antennae aim toward the Earth. They use no 
jets since their planet bypasses. 
    When the various missions to Pluto were planned in the late 1990s, 
one function was to investigate the Pioneer anomaly with dedicated 
instruments. However, the only Pluto mission commissioned was New 
Horizons, launched in January 2006. It took one swingby of Jupiter in 
February 2007 and is now on a recession path from the Sun. 
    New Horizons can not be used for Pioneer effect examination 
because of the intermittent and complex radio system it carries. With 
nothing to do until it reaches Pluto in 2015, New Horizons is 
hiberating for almost the entire journey from the Jupiter flyby until 
then. Once every few months it automaticly wakes up to send a short 
message of vital measurements back to Earth. After these are 
acknowledged and OKed by Earth, the craft returns to sleep. 
    Other missions, like Galileo, Cassini, Ulysses, suggest the 
anomaly affects them, too. Their trajectories and comms are too varied 
and complex for a 'clean' confirmation. 
    This leaves ONLY the two Pioneer data archives for future inquiry 
into the Pioneer anomaly. 
    In vernacular speak, an 'acceleration' is a speedup of motion. To 
describe a slowdown of motion, the word is 'deceleration'. In physics 
only the term 'acceleration' is used for both changes of speed. The 
slowdown of speed is handled by a negative value of acceleration.
    One reason to have only the one concept is that acceleration is a 
vector. Unless there are deliberate conditions that confine motion to 
a linear path, like a train on its tracks, it can not be assumed that 
a deceleration is opposite to an acceleration. On a spaceship, the 
push, by firing the rockets, can be in any direction relative to the 
forward motion. The idea of a unique sense of deceleration loosens up. 
    In the Pioneer cases, the craft are moving almost radially away 
from the Sun and are suffering a slowdown or deceleration. They are 
not going as fast as they are calculated to move. Yet we speak of the 
anomaly as an excess acceleration, which can be taken for a speeding 
up beyond the calculated motion. This jargon can confuse some 
listeners at first. 
    Acceleration is a vector, like velocity. To completely specify 
acceleration a direction must be included in addition to its 
magnitude. In the usual popular discussions, this feature of the 
pioneer anomaly is commonly missed out. In fact, the value of the 
excess acceleration is prevalently cited with no signum, neither plus 
nor minus. 
    Because the monitoring of the excess is done solely by radial 
velocity measurements from the received frequency of the Pioneer 
signals, only the line-of-sight component is known. There could be a 
component in the tangential plane but this is for the Pioneer craft 
not sensible. The trajectory is so nearly radially from the Sun that 
there is no proper motion in the tangent plane to work out a 3D model 
of the anomaly. 
    Because the value is about the same for both Pioneers and is 
arguibly also the same for other spacecraft, the feeling is that the 
entire vector is more or less aimed back to earth. Assuming that the 
outward direction is positive, the anomaly carries the negative 
signum. For a reverse signum convention, the anomaly is positive. 
    However, the direction of the vector is uncertain and could be one 
of at least four according as the hypothesized cause. It could be 
aiming at the Sun, aiming at the Earth, aligned with the flightpath, 
aligned with the craft spin axis.
    It turns out that all four are close within a couple degrees due 
to the remoteness of the craft from Sun and Earth, the deliberate 
pointing of the spin axis toward Earth, and the linearly outward track 
of the ship. 
Missing records 
    One of the disgusting realities of human endeavors is the 
haphazard way we preserve our history an legacy. This is specially 
prevalent with so much of human information collected and stored on 
fragile media and read by proprietary devices. Both have short 
lifetimes, of a decade or so! 
    Paper records are not exempt from short life. Old books and 
blueprints are often discarded or lost after their use is deemed over 
and done. In particular, working papers, often with crucial 
annotations and side calcs, are routinely tossed after the final 
formal report for the project is issued. 
    The panel brought out two instances associated with the Pioneer 
anomaly. One potential source for the acceleration is thermal recoil 
force. The internal parts of the spacecraft produce heat radiation. 
When this is released from the outer surface of the ship, a tiny 
recoil force is produced. To study this effect, a complete and 
accurate description of the craft is required. It turns out that JPL 
did lose, by misplacement or rearrangement of offices, many of the 
prime paper records for the Pioneers. It become a 'treasure hunt' to 
find these paper and speak with project workers. The thermal 
specification of the Pioneers is still incomplete but encouraging. 
About 70% of the anomaly can be traced to thrust-producing thermal 
radiation. The leftover 30% could be found in the missing records. 
Ancient computer 
    The radio reception from the Pioneers was stored on magnetic 
tapes, of the old 9-track kind so prevalent in mainframe computer 
centers of the 1960s. The computers that read these tapes are by the 
1980s almost entirely replaced by other models that did not use these 
tapes. Hence, the material was orphaned, so to speak, with no way to 
even look at them. 
    This situation is prevalent thruout the space program and even 
other large-scale government and corporate operations. As computers 
are replaced, only certain data, often in a half-hearted way, are 
transferred to new media accommodated by the new machines. The result 
is that orphaned information ends up abandoned and eventually 
    On the home computer scale, this is happened twice in the last ten 
years. First, the former 120mm 'floppy' discs were replaced by the 
90mm 'stiffy' discs in the 1980s. New home computers no longer had the 
floppy discdrive, rendering all the old floppies useless. 
    Today, the 90mm discs are phasing out in favor of CDs, with 
current computers having no stiffy discdrive or only an accessory one. 
    In addition to the media problem, the issue of actually getting 
intelligence from the 0/1 pattern remains. The paper instructions 
telling how the information is written and what the encoded values 
mean may be lost or otherwise not to hand. So it is not at all a 
matter of simply ordering -- and funding -- a study of the Pioneer 
Defying physics?
   One very common feature of a discussion of the Pioneer effect is 
its disobedience of physics. This notion leads to weird ideas of 
forces outside present science, and into the field of parascience and 
nonscience. There is a distinction to be emphasized here. 
    One is that there is an unknown, but ultimately discoverable, 
gravity force. This force, from some distribution of ordinary mass, 
produces the observed extra acceleration. This mass can be 
concentrated in a few bodies or diffused in a gas or dust region. It 
could be in the 'dark matter' permeating the Milky Way. 
    The other is that there is an unknown, but discoverable, 
nongravity force out there. Gravity is only ONE kind of force; there 
are hundreds, if not thousands, of other influences that do not arise 
from gravity. The thermal thrust idea is but one. An other may be 
thrust-producing leak from the residual fuel. The latter would be 
unknown because we can not examine the craft close up and there are no 
leak-monitoring instruments on it. 
Two examples
    Tyson, in his role as animateur for the debate, put out two 
examples where solar system bodies with anomalous trajectories led to 
an ordinary and extra ordinary solution. The deviation of Uranus from 
its gravitational path, as calculated from the forces of the other 
known planets, eventually yielded the new planet Neptune. There was no 
'new physics' but a smashing victory for the existing science. 
    The deviation of Mercury's motion failed to turn up any new 
bodies, provisionally named Vulcan. It generated an allnew science, 
the Einstein relativity theory. 
    Which way will the Pioneer anomaly take us? 
Curious calculation
    Dr Belbruno offered a curious calculation. He worked out the 
effect of the Milky Way on the solar system. Using reasonable values 
for the mass of the galaxy and our radius from its center, he got, 
rounded, 8e-10m/s2! This is precisa mente the value of the Pioneer 
    He emphasized this was a rough calc, only for the magnitude, and 
it is the gravity field strength at the solar system. It holds the 
solar system in galactic orbit. He also didn't know off hand the 
vector direction of the Pioneer ships from the galactic center. 
    He cited 400 billion suns mass and 27,000 lightyear radius. From 
these and the usual formula for the gravity field strength, I get
  GFS = gamma*(400 billion suns)/(27,000ly)^2
      = (6.67e-11n.m2/Kg2)*((400e9)*(1.99e30Kg/sun))
      = 8.14e-10m/s2
Belbruno's math checks. His mass of about 400 billion suns is a 
recognition of the dark matter within the galaxy. 
    The banter from the panel indicated that what is really needed is 
the differential force on the Pioneer, due to its slightly farther 
radius from the galactic center. By luck it is heading about in 
opposition to the galactic center. The easiest ay to get this is to 
take the derivative of the GFS formula, to obtain the change in 
strength per meter of radius. 
  1der(GFS, radius) = (-2)*gamma*(400 nillion suns)/(27,000ly)^3 
                    = (-2)*(6.67e-11n.m2/Kg2)
                    = (-6.40e-30m/s2)/m 
    For the extra radius out for Pioneer, 92AU, I get
  diffGFS = (-6.40e-30m/s2)/m*(92AU)*(1.49e11m) 
          = -8.77e-17m/s2 
    This is the differential, or tidal, acceleration of Pioneer 
relative to Sun due to tide action of the Milky Way. This is too low 
by a factor of ten million. 
    More than that, as a tidal acceleration, it tends to move the 
spacecraft FASTER away from the Sun, not slower. Or, the Sun falls a 
bit faster than Pioneer, leaving the ship behind, farther away than if 
they fell at the same rate. A similar reasoning applies if Pioneer 
were heading toward the galactic center; it falls faster than SUn, 
pulling away from it. 
    The above discourse derives from the dialog at the lecture. In the 
days following the lecture, Dr Belbruno pointed out to me that the 
impression offered above is misleading. In the brief moment of his 
comments he missed out details of a larger idea he holds. 
    The acceleration of 8e-10m/s2 is not just a coincidence, but is 
the actual value; the galaxy itself is partly the CAUSE of the Pioneer 
    What is belbruno's idea? 
    He didn't get the chance to lay it out at the debate. No one else 
on the panel caught on to it. He didn't elaborate it in his later 
comms with me. He will present it at the 'New trends in astrodynamics' 
conference on 27-29 June 2007 at Princeton University. Information 
about this conference is at ''.
    End of June is only 3 months from end of March, when the Asimov 
debate took place. It's a long 3 months to wait; wait we must. 
Overall consent
    None of the panelists argued for a new branch of physics. All 
allowed that the Pioneer effect seems to be solvible within present 
science. It will be increasingly harder to study the problem because 
there is no hope of gathering new data -- the spaceship are both out 
of action -- and eventually the data in house will decay or be 
abandoned. The panel agreed that the existence of the anomaly, while 
being an intriguing problem of science, will not impede the future 
exploration of the solar system. It is just too small to louse up 
spaceship trajectories, specially if the craft has propulsion. 
Future work?
    Can the anomaly be confirmed by tracking natural objects in the 
outer solar system like planet Pluto or Kuipeer body? Not really. The 
effect comes out from comparing the calculated path with the observed 
one and the observed path must be ultra accurate. So much so, that 
only, so far, radio or other electronicly processed frequency, is able 
to bring out the truly minute excess acceleration. Pluto and Kuiper 
bodies arre observable only in the optical or adjacent IR band and 
their astrometry is still rather loose. Further more, we then obtain 
where these objects are with no way to predict where they should be. 
    How about sending out a dedicated new vessel for just probing the 
Pioneer effect? ESA in 2004 had such a mission on the drawing boards, 
but it was soon called off. This would be perhaps the best method of 
attacking the problem, but it still is a $200 million project for the 
satellite and launch. In today's funding constraint there is no hope 
of such a mission soon.
    Rescue of the Pioneer data archive is imperative, not only for the 
anomaly. In general, NASA has warehouses of old electronic media that 
it no longer can extract data from and no longer knows what the data 
are. By good luck, there can be a retired computer that can readout 
the media and transfer their contents to new ones. In most situations, 
no such fortune prevails. 
The solution
    The Asimov panel offered no definite solution, but gave the 
audience th feeling that the anomaly is a situation under control and 
accounted for. In the absence of having the Pioneer craft on a lab 
bench, glitches in it probably will never be uncovered, however 
ordinary they may be. Even so, it does not explain how the excess 
acceleration is, as far as the extant records can show, a constant 
amount regardless of distance, direction, duration for all the 
spacecraft affected by it.
    And so, it could be that pioneer-10 an Pioneer-11 will sail into 
the interstellar abyss, taking their secret with them.